A transportation problem has 8 origins and 7 destinations. The optimal solution of this problem will fill no more than ________ cells with quantities to be shipped.
A) 2
B) 13
C) 14
D) 48
E) Cannot be calculated without knowing the supply and demand totals.

Question

Quizplus · Accepted Answer

The maximum number of cells that can be filled with quantities to be shipped is the total number of origins multiplied by the total number of destinations, which gives 8 x 7 = 56. However, since this is an optimal solution, there will be at least one origin or destination that is not used, which means that the maximum number of filled cells is 56 - 7 = 49. Since not all origins will necessarily have supply and not all destinations will necessarily have demand, we cannot determine the exact number of cells that will be filled without additional information. However, we can be certain that it will be no more than 49. Therefore, the correct answer is C (14), which is the closest option to 49.

A Transportation Problem Has 8 Origins and 7 Destinations